Cornell College
STA 363 Fall 2024 Block 1
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
Logistic regression
\[\begin{aligned}\pi = P(y = 1 | x) \hspace{2mm} &\Rightarrow \hspace{2mm} \text{Link function: } \log\big(\frac{\pi}{1-\pi}\big) \\ &\Rightarrow \log\big(\frac{\pi}{1-\pi}\big) = \beta_0 + \beta_1~x\end{aligned}\]
Generalized Linear Models (Ch 1 - 6)
Modeling correlated data (Ch 7 - 9)
More Regression Models (ITSL Chapter 7) - Polynomial Regression - Regression Splines - Smoothing Splines - Generalized Additive Models (GAMS)
Reporter will share list with the class
Pre-reqs
Background knowledge
Lectures
Attendance is expected (if you are healthy!)
Beyond Multiple Linear Regression by Paul Roback and Julie Legler
The secondary text is: An Introduction to Statistical Learning with Applications in R by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani – it is freely available online. Chapter 7.
Readings
Homework - Primarily from Beyond Multiple Linear Regression - Individual assignments - Work together but must complete your own work. Discuss but don’t copy.
Mini-projects
Examples:
Two exams this block, September 6th and 18th.
Each will have two components
Final grades will be calculated as follows
| Category | Points |
|---|---|
| Homework | 200 |
| Participation | 100 |
| Labs and Mini Projects | 300 |
| Exams | 400 |
| Total | 1000 |
See Syllabus on website for letter grade thresholds.